please finish the questions without any programming.3)LetX, Y be two continuous random variables with joint density function 8 xy / q 4if0 < y < x< q f(x,y½q)= otherwise . We want to estimate q relative to Mean Square Error (MSE).From lecture we already know that X is a sufficient statistic forq and has density function fX (x½q)=4 x3 / q4 if0 < x < q 0 otherwise Consider the estimatord (x,y) =3 x y. Without computing any MSE find an estimator that will have smaller MSE than the estimatord (x,y)=3 x y and explain why that should be true. 4)We have one observation,Y,having pdf, for -1≤q≤1, equal to 2 y q + 1if-1/2<y<1/2 f (y½q)= 0otherwise. NOTE:For f (y½q) to be a density function the only possible values ofq must be in the closed interval -1≤ q≤1. Consider the estimator W(y) defined as W( y)= 1ify³0 -1ify <0 a.IsW(y)an unbiased estimator ofq? b..Show that W(y) is an MLEofq.
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